Identify Coefficients in x² + 7x = 0: Component Analysis

Q: How do I find the constant term when it's not there?

If there's no constant term visible in the equation, then c = 0. Remember, $ x^2 + 7x = 0 $ is the same as $ x^2 + 7x + 0 = 0 $.

Q: What's the difference between a term and a coefficient?

A term includes everything: the number AND the variable (like $ 7x $). A coefficient is just the number part (like 7). Think of coefficients as the 'multipliers' of the variables.

Q: Do I always need to write the equation in standard form?

For identifying coefficients, yes! Standard form $ ax^2 + bx + c = 0 $ makes it easy to spot each coefficient. If your equation equals something other than 0, move everything to one side first.

Quadratic Coefficients with Standard Form

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$x^2+7x=0$

What are the components of the equation?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 These are the coefficients

00:03 Let's write the quadratic equation formula

00:11 The coefficient of X squared is A

00:15 The coefficient of X is B

00:19 And the constant number is C

00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$x^2+7x=0$

What are the components of the equation?

Step-by-step solution

Let's solve the problem step-by-step:

First, consider the given equation:

$x^2 + 7x = 0$

This equation is almost in the standard form of a quadratic equation:

$ax^2 + bx + c = 0$

Where:

$a$ is the coefficient of $x^2$
$b$ is the coefficient of $x$
$c$ is the constant term (independent number)

Let's identify each of these components from the given equation:

For $a$ : The term with $x^2$ is $x^2$ . In this case, the coefficient is implicitly 1, so $a = 1$ .
For $b$ : The term with $x$ is $7x$ . The coefficient of $x$ is 7, so $b = 7$ .
For $c$ : There is no independent constant term visible, so we assume $c = 0$ .

Thus, the components of the quadratic equation are:

$a = 1$ , $b = 7$ , $c = 0$

The correct choice from the provided options is : $a=1$ , $b=7$ , $c=0$

Final Answer

$a=1$ $b=7$ $c=0$

Key Points to Remember

Essential concepts to master this topic

Standard Form: $ax^2 + bx + c = 0$ identifies all three coefficients
Technique: When coefficient appears invisible like $x^2$ , it equals 1
Check: Substitute coefficients back: $1x^2 + 7x + 0 = x^2 + 7x$ ✓

Common Mistakes

Avoid these frequent errors

Confusing terms with coefficients
Don't say a = x² or b = 7x = wrong identification! Terms include the variable, but coefficients are just the numbers. Always separate the number (coefficient) from the variable part.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Why is the coefficient of x² equal to 1 when I don't see any number?

When no number appears before a variable, the coefficient is implicitly 1. Think of $x^2$ as $1 \cdot x^2$ - the 1 is just not written!

How do I find the constant term when it's not there?

If there's no constant term visible in the equation, then c = 0. Remember, $x^2 + 7x = 0$ is the same as $x^2 + 7x + 0 = 0$ .

What's the difference between a term and a coefficient?

A term includes everything: the number AND the variable (like $7x$ ). A coefficient is just the number part (like 7). Think of coefficients as the 'multipliers' of the variables.

Do I always need to write the equation in standard form?

For identifying coefficients, yes! Standard form $ax^2 + bx + c = 0$ makes it easy to spot each coefficient. If your equation equals something other than 0, move everything to one side first.

What if the coefficient is negative?

Negative coefficients are perfectly normal! For example, in $x^2 - 3x = 0$ , we have a = 1, b = -3, c = 0. The negative sign is part of the coefficient.

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